Glavin, SE; (2012) Mathematical modelling of urethral and similar flows. Doctoral thesis , UCL (University College London).

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Abstract

Flows in flexible tubes and vessels have been studied extensively in the past with particular application to the cardiovascular and respiratory systems. However there have been few treatments of the lower urinary tract, which consists of the bladder and urethra. This thesis concentrates specifically on the urethra with the aim of giving insight into the evolving flow characteristics within the vessel and mechanical responses of the vessel which give rise to fluid structure interactions. Urethral modelling is an important area of research given the social and economic costs involved in lower urinary tract dysfunction. In the modelling, examination is given to slow and fast opening vessels where certain exact analytical solutions are found along with numerical results. Following this, fast and slow responses of the walls of the vessels are considered, where the response is defined as the relative change in cross-sectional area for relatively varying transmural pressure. These features are important for pathologies that alter the characteristics of the vessel wall such as bladder outlet obstruction. A change in the distensibility along the vessel resulting from pathologies or normal transition through the various sections of the urethra is studied both in terms of developing jump conditions based on a localised Euler region and also over a comparatively short length scale giving rise to the Burgers equation; small amplitude instabilities are studied through the derivation of the KdV equation. Following on from these mostly two-dimensional treatments, three-dimensional systems are then studied. Consideration is given to the secondary flow effects driven by the tortuosity of a vessel in three dimensions. We study cases of three-dimensional constriction, with main interest in the effects of benign prostate hyperplasia or urethral stricture on the flow, where pressure drops are demonstrated. Finally an appendix deals with the effects concerned with a wide population, focusing on an allied problem of consumer choice.

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